ROTATE Break Into Groups

CONNECT

DO NOW!

Brain TeaserSolve this riddle.›Vicki is in elementary school. She is exactly half the age of her sister. What could be the ages of Vicki and her sister?

Vicki could be years old.

Her sister would be years old.

1 1

.

3 3 178

Equation 1 ª

Equation 2 ª

Equation 3 ª

3 3 178 5

100 70 8

3 Π100 3 Π70 3 Π8

8100 70

3

3 Π100 = 300 3 Π70 = 210

3 Π8 = 24

= 300 = 210 = 24

300210+ 24500+ 30+ 4534

534

GROUP

CLASS

CONCEPT

Using place-value understanding to estimate enables stude nts to focus on whether their answers make sense.

Sushi Monster Chapter 1

mSpace pages 68, 72–73

Instructional Video “Estimate and Compare Products”

■ Expr essions & Equations Use properties to generate equivalent expressions.

■ Make use of structure. ■ Construct viable arguments.

■ Apply properties of operations as strategies to multiply.

■ Multiply a whole number up to four digits by a 1-digit whole number.

■ Understand the term estimate and use it to explain the reasonableness of an answer.

■ Apply the Distributive Property when multiplying 1-digit by 3-digit factors.

■ Apply place-value understanding to estimate and compare products.

Estimate and Compare ProductsStudents decompose the 3-digit factor when multiplying 1-digit by 3-digit facto rs.

Split a 3-Digit Factor Yesterday we learned to split rectangles without a grid to multiply with a 3-digit factor.

Explain the example from Block 2, Topic 2, Lesson 1.

What strategy did we use to split the rectangles? (We split the 3-digit factor by place value into hundreds, tens, and ones, and then split the rectangle to match those numbers.)

Today, we will multiply 1-digit by 3-digit factors by splitting numbers instead of rectangles.

M ATHEMATICAL PRACTICE Make Use Of Structure

Students solve a problem with multiple solutions and analyze the relationship among the numbers to identify a pattern.

Ask several students to share solutions using the sentence frame. (Vicki could be any age between 5 and 12 years old; her sister would be twice that age.)

Use Turn & Talk to discuss a variation of the riddle.

If Vicki’s sister attends high school, what ages could Vicki be? (Most high school students are between ages 14 and 19. Since Vicki is half the age of her sister, Vicki could

be between the ages of 7 and 9.)

Develop Flexible Thinking Page 68

HOMEWORK (optional)

Language Goals

Content Objectives

2 CONCEPT

1 CONCEPT

3 CONCEPT

4 GAME

5 PROBLEM SOLVING

Application

Teacher-DirectedTOPIC TRACKER

GRADE-LEVEL CONTENT CONNECTIONS

CORE WITHIN THE CORE

MATHEMATICAL PRACTICES

LESSON 2TOPIC 2BLOCK 2

98 MATH 180 Block 2 › Topic 2 › Lesson 2

104-107_m180_tli_11_b2t2l2.indd 98 1/22/13 10:50 AM

TEACH

3 3 487

3 5Estimate: 3 500 15003 500 1500

3 3 487

3 5Estimate: 3 500 1500

3 Π(400 + 80 + 7)3 Π(400 + 80 80 + 7) 7)

3 3 487

3 5Estimate: 3 500 1500

3 Π(400 + 80 + 7) (3 Π400) + (3 Π80) + (3 Π7)

3 Π400 = 1200 3 Π80 = 240 3 Π7 = 21

(3 Π400) + (3 Π80) + (3 Π7)

3 Π400 = 12003 Π80 = 2403 Π7 = 21

3 3 487

3 5Estimate: 3 500 1500

3 Π(400 + 80 + 7) (3 Π400) + (3 Π80) + (3 Π7)

3 Π400 = 1200 3 Π80 = 240 3 Π7 = 21

Is your answer reasonable?

3 3 487 5yes

1400601

1461

1461

+

yes

1400601

1461+

1461

GROUP

Add the Partial Products.

Now I’ll add the partial products to get the product.

Think aloud as you add the partial products using place value and display the sum.

What is the total product? (1461)

Display the equation 3 × 487 = 1461.

MODEL REASONING Finally, I compare the product to my estimate of 1500. Since 1461 is close to my estimate, my answer is reasonable.

Ask a student to record “yes” in the blank.

Find the Partial Products.

Now we’ll apply the Distributive Property. We rewrite the expression to multiply 3 times each part of 487.

Display the expression on screen. Use Answers Up to have students multiply the partial products. Record the equations as students share answers.

What is 400 × 3? (1200) What is 80 × 3? (240) What is 7 × 3? (21)

MODEL REASONING I aligned the partial products using place value. This will help me add correctly.

Rename the 3-Digit Factor.

MODEL REASONING Now I will split 487 by place value. How should I split 487? (400 + 80 + 7)

Instead of splitting a rectangle, I will use the Distributive Property to find the product. So I wil l multiply 3 times each of the parts of 487.

Display 3 × (400 + 80 + 7).

I used parentheses to show that 3 is multiplied by all of the parts of 487.

Model How to Estimate and Compare › Play the Instructional Video for this lesson.

STRATEGIES FOR MULTIPLICATION

Estimate the Product. VOCABULARY Before I find the product of 3 × 487, I will make an estimate. An estimate is an approximate or “about” product.

Then I’ll solve the problem and compare my answer to the estimate. If the estimate is close to my answer, I can say that my answer is reasonable.

MODEL REASONING When I make an estimate, I want numbers that I can easily multiply mentally. 487 is between 400 and 500, but closer to 500. So, I’ll make an estimate by multiplying 3 × 500.

Estimate and Compare Products 99

104-107_m180_tli_11_b2t2l2.indd 99 1/22/13 10:50 AM

RR

6 3 723

3 5Estimate:

Is your answer reasonable?

6 3 723 5

6 700 42006 700 4200

R

6 3 723

3 5Estimate:

Is your answer reasonable?

6 3 723 5

6 700 4200

RRRRRRRRRRRR

6 Π(700 + 20 + 3)6 Π(700 + 20 20 + 3) 3)

R

6 3 723

3 5Estimate:

Is your answer reasonable?

6 3 723 5

6 700 4200

R

6 Π(700 + 20 + 3)

RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR

(6 Π700) + (6 Π20) + (6 Π3)

6 Π700 = 4200 6 Π20 = 120 6 Π3 = 18

(6 Π700) + (6 Π20) + (6 Π3)

6 Π700 = 42006 Π20 = 1206 Π3 = 18

R

6 3 723

3 5Estimate:

Is your answer reasonable?

6 3 723 5

6 700 4200

R

6 Π(700 + 20 + 3)

R

(6 Π700) + (6 Π20) + (6 Π3)

6 Π700 = 4200 6 Π20 = 120 6 Π3 = 18

RRRRRRRyes

4300308

4338

4338

+

yes

4300308

4338+

4338

GUIDED PRACTICE GROUP

Estimate and Compare Products (continued)

Add the Partial Products.

Now we can add the partial products to find the total product. What is 723 × 6? (4338)

Have students Think-Pair-Share to compare the product to the estimate and explain whether or not the answer is reasonable. (The answer is reasonable because 4338 is close to the estimate of 4200.)

Find the Partial Products.

Let’s rewrite the expression to show that we’re mutiplying 6 times each part of 723.

Ask a student to rewrite the expression as shown.

Use Answers Up to find the partial products.

What is 700 × 6? (4200)

What is 20 × 6? (120)

What is 3 × 6? (18)

Check that students align the partial products by place value as they do their work in their mSpaces .

Rename the 3-Digit Factor.

We’ll start by splitting 723. How can we rewrite 723 using place value? (700 + 20 + 3)

How can we rewrite the expression using the Distributive Property? 6 × (700 + 20 + 3)

Have students record the expression in their mSpaces . Then ask a student to record it on screen.

LANGUAGE DEVELOPMENT Estimate is used throughout this lesson as both a noun and a verb. Have students look up estimate in the glossary. Then, describe the difference between the two definitions to help them understand the distinction.

Estimate the Product.

Let’s do the first problem together: 6 × 723.

First, we’ll estimate the product .

VOCABULARY Display and read aloud the definition of estimate . Have students repeat the term.

To estimate this problem, I know that 723 is between 700 and 800. Is 723 closer to 700 or 800? (700)

We’ll use 700 to estimate. What is 6 × 700? (4200)

Ask a student to record the estimate on screen, and have students record it in their mSpaces.

Page 72 Solve Problem 1 Together

Lead a Discussion Ask, Does the Distributive Property work when multiplying any numbers? Can you use it to multiply 4 × 5?

BLOCK 2 › TOPIC 2

LESSON 2

100 MATH 180 Block 2 › Topic 2 › Lesson 2

104-107_m180_tli_11_b2t2l2.indd 100 1/24/13 5:08 PM

Exit Ticket Exit TicketExit Ticket Answer this question.>

Is 5600 a reasonable estimate for the product of 7 3 841? Why or why not?

SUMMARIZE & ASSESS

PRACTICE

GROUP

PAIRS

SCORE

3 4

BLOCK

2›› Answer this question.

Is 5600 a reasonable estimate for the product of 7 3 841? Why or why not?

5600 is/is not a reasonable estimate for the product of 7 x 841 because

4 3 438

Estimate: 3 5

4 3 438 5

Is your answer reasonable?

7 3 296

Estimate: 3 5

7 3 296 5

Is your answer reasonable?

If my estimate is close to the product I found,

I know my solution is probably correct.

estimate (n) A number that is close to the exact answer.

estimate (v) To approximate a calculation using numbers that are easier to work with.

Strategies for Multiplication 73

7 300 2100 4 400 1600 841 is close

to 800. So I multiplied 7 by 800

to get an estimate of 5600. 7 × (200 + 90 + 6) (7 × 200) + (7 × 90) + (7 × 6) 7 × 200 = 1400 7 × 90 = 630 7 × 6 = 42

1400 630 + 42 2072

4 × (400 + 30 + 8) (4 × 400) + (4 × 30) + (4 × 8) 4 × 400 = 1600 4 × 30 = 120 4 × 8 = 32

1600 120 + 32 1752

2072 1752

yes yes

1 2

Estimate the product.

5 3 614

Estimate: 3 5

Rename the 3-digit factor.

Find the partial products

Add the partial products.

5 3 614 5

Is your answer reasonable?

Estimate the product.

6 3 723

Estimate: 3 5

Rename the 3-digit factor.

Find the partial products

Add the partial products.

6 3 723 5

Is your answer reasonable?

Add the partial products.

1200 240 + 21 1461

3 3 487 5 1461 Is your answer reasonable? yes

Find the partial products.

(3 × 400) + (3 × 80) + (3 × 7) 3 × 400 = 1200 3 × 80 = 240 3 × 7 = 21

Rename the 3-digit factor.

3 × (400 + 80 + 7)

Estimate the product.

3 3 487

Estimate: 3 3 500 5 1500

Estimate and Compare Productsconceptlesson 2

Topic 2Block 2

72 Math 180 Block 2 › Topic 2

6 700 4200 5 600 3000

6 × (700 + 20 + 3) 5 × (600 + 10 + 4)

(6 × 700) + (6 × 20) + (6 × 3) 6 × 700 = 4200 6 × 20 = 120 6 × 3 = 18

(5 × 600) + (5 × 10) + (5 × 4) 5 × 600 = 3000 5 × 10 = 50 5 × 4 = 20

4200 120 + 18 4338

3000 50 + 20 3070

4338 3070

yes yes

Pages 72–73 Solve Problems in Pairs › Project the mSpace and have students work collaboratively as you circulate.

Modify Tasks

IF students struggle with making reasonable estimates,

THEN provide them with simpler problems.

■ Avoid 3-digit factors that are close to halfway between two multiples of 100.

■ Use 3-digit factors such as 302, 497, and 615.

Respond to Common Patterns of Thinking

IF students don’t align the partial products by place value, THEN show an example with partial products aligned by place value.

■ Demonstrate that there is less chance of error when adding the hundreds, then the tens, and then the ones.

Elicit Student Thinking

Ask questions to help students explain their strategies for making estimates.

■ Why did you change the factor to make an estimate?

■ Can you explain how you know your estimate is reasonable?

Page 73

Review Estimating and Comparing Products MATHEMATICAL PRACTICE Construct Viable Arguments

Students evaluate an estimate for a product and explain in detail whether it is reasonable.

Today we learned how to estimate products and to multiply with 3-digit factors using the Distributive Property.

As your exit ticket, answer this question and write your response in complete sentences.

STRATEGIES FOR MULTIPLICATION

Estimate and Compare Products 101

104-107_m180_tli_11_b2t2l2.indd 101 1/22/13 10:50 AM